Integrated optical circuits are poised to open up an array of novel applications. A vibrant field of research has emerged around the monolithic integration of optical components onto the silicon substrates. Typically, single mode optical fibers deliver the external light to the chip, and submicron single-mode waveguides then guide the light on-chip for further processing. For such technology to be viable, it is critically important to be able to efficiently couple light into and out of the chip platform, and between the different components, with low losses. Due to the large volume mismatch between a fiber and silicon waveguide (on the order of 600), it has been extremely challenging to obtain high coupling efficient with large tolerance. To date, demonstrated coupling has been relatively lossy and effective coupling requires impractical alignment of optical components. Here, we propose the use of a high contrast metastructure (HCM) that overcomes these issues, and effectively couples the off-chip, out-of-plane light waves into on-chip, in-plane waveguides. By harnessing the resonance properties of the metastructure, we show that it is possible to spatially confine the incoming free-space light into subwavelength dimensions with a near-unity (up to 98%) efficiency. The underlying coupling mechanism is analyzed and designs for practical on-chip coupler and reflector systems are presented. Furthermore, we explore the two-dimensional HCM as an ultra-compact wavelength multiplexer with superior efficiency (90%).
© 2017 Optical Society of America
Ultra-compact photonic integrated circuits (PICs) have the potential to replace the conventional electronic integrated circuits and revolutionize a variety of technologies. Built from submicron-sized silicon photonic wires that carry light, PICs offer faster processing speed, a more compact size and the ability to integrate different optical functionalities onto a single chip. They are promising for applications ranging from light-based communication to interconnect to low-cost lab-on-a-chip systems [1, 2]. For practical purposes, it is important to be able to couple external light (from an optical fiber, free-space optics or device such as a laser) onto the chip efficiently and into on-chip waveguides for further use. However, single-mode silicon waveguides and external, out-of-plane light beams usually differ in size by two orders of magnitude. As a result, coupling efficiency is normally low and ultra-precise optical alignment of the components is necessary to achieve a level of useful coupling. This severely constrains the ability to test and package such systems, and therefore their practicality.
To date, efforts have been made to use inverse tapered waveguide to improve the coupling between on-chip waveguides and external light beams [3, 4]; however there are a number of drawbacks with such approaches. Typically, specialized optical fibers and cleaved devices with polished facets are required. Very precise optical alignment and therefore custom device packaging is needed, which drastically increases the cost. Diffraction-grating-based light couplers have been studied extensively and are attractive because of their planar fabrication process and the ability to test their performance on the wafer-scale. However, while the optical coupling happens in the second-diffraction order, the principal diffraction order always exists and leads to light coupling with an efficiency that is decibels from unity [5–8]. Furthermore, this low coupling efficiency usually goes hand in hand with strong reflection to the incident light source, which poses an additional challenge given the difficulty of introducing an optical isolator into the compact integrated optical system.
In this work, we report that the resonant properties of a high contrast metastructure (HCM) can be used to achieve extremely efficient coupling of out-of-plane light waves into an in-plane waveguide. The HCM consists of a periodic structure made of high refractive index material, which is fully surrounded by the low index materials. The period of the metastructure is smaller than the wavelength of interest. It offers broadband ultra-high reflectivity and a high quality-factor (Q-factor) resonance [9–12]; the resonance process has already been observed experimentally . In addition, more applications are explored to implement this structure to the flexible substrate, forming a color-controllable flexible membrane . When the HCM is working as a resonator, the incoming free-space-propagation light is trapped inside the near-subwavelength periodically-structured region, where it is forced to bounce back and forth many times before it is diffracted (principal-order diffraction) and leaves the structure. We propose using this resonant behavior to boost the coupling between light propagating in in-plane waveguides and light propagating out-of-plane. Furthermore, the proposed HCM coupler can efficiently couple the incidence light from multiple in-plane directions to the normal direction simultaneously. We utilize this property to design an ultra-compact wavelength multiplexer with 90% efficiency and broadband continuous wavelength response.
2. Coupling mechanism
In general, for diffraction-grating couplers, incident light with an angle with respect to surface normal direction is spatially modulated in the x-direction by the periodic structure (Fig. 1). At the exiting plane, the light field can be expressed as , where is the amplitude of the mth diffraction order obtained from Fourier transform calculations and is the propagation constant in vacuum. For a waveguide mode with effective refractive index , the phase will be matched between that of the near-field light wave of the HCM cavity and the waveguide mode if , where is the refractive index above the incidence plane. Light thus couples into the waveguide with a coupling efficiency with phase matching. Because is always smaller than for a waveguide, the coupling order m has to be larger than 0. Typically, m is chosen to be 1 to minimize the light leakage to other higher diffraction orders. However, as the 0th order term always exists and has a real propagation component in the z-direction, the energy carried in this order is lost during the coupling process. This “directionality problem” is a fundamental issue for grating-based waveguide couplers .
To solve this problem, one can set up an optical cavity in the z-direction in order to prevent the light from escaping in the 0th order before coupling into the waveguide. The cavity confines the light and thus forces the photons to undergo a much longer interaction with the coupler. Let us assume that light traverses the cavity an average of N times before escaping, the coupling efficiency for each single trip is . The enhanced coupling efficiency would then be , which exponentially approaches unity if N is sufficiently large, determined by the optical cavity quality factor. Previous work has proposed the use of a reflector below the waveguide structure to prevent 0th-order diffraction on the light transmission side . However, from a practical standpoint it is not very convenient to place the other reflector at the incidence side (), as incoming light is usually delivered by an optical fibre, free-space optics or the other light sources. Thus setting up the resonance in the z-direction within the coupler itself is the ideal approach to suppressing the 0th-order diffraction and therefore maximizing light coupling efficiency.
We now turn to the resonant behavior inside the high-index-contrast structure. For a periodic single-layered structure without a waveguide underneath, we can assume HCM is infinite in the y-direction and infinitely periodic in the x-direction. It can thus be considered as an array slab waveguide that supports an array of eigen-modes propagating along the z-direction; let us denote the propagation constant as . Due to the large refractive index contrast, there exists a broad range of incident light wavelengths for which only two even modes, with corresponding propagation constants and , are supported for light incident at 90° to the surface. We denote this wavelength range as two-modes region. For oblique angle incidence, an additional odd mode, with propagation constant , will appear. Because the array eigen-modes are orthogonal to one another, they will not couple during propagation. However, when the modes reach the HCM interface at and and experience an abrupt refractive index change, they will be reflected back to themselves and as well as coupled to one another. From a cavity perspective, the array waveguide eigen-modes can be orthogonalized into “supermodes” with propagation constant ,. Denoting the phase accumulation of a supermode during a single half-round-trip through the cavity as , the Fabry-Perot resonance condition for the phase is , where n is an integer. In the two-modes region, if both modes satisfy the Fabry-Perot resonance condition and arrive at the exit interface in phase (with a phase difference of an even multiple of ), the resonance will be greatly enhanced. Detailed calculations are reported in .
With this mechanism in mind, we can now optimize the design of the set-up for maximal light coupling onto the photonic circuit. We first plot the reflection spectra of a single-layer HCM resonator at as a function of HCM thickness without waveguide structure for surface-normal incidence, shown in Fig. 2(a) and 10°-oblique-angle incidence, shown in Fig. 2(b). For display purposes, both HCM thickness and wavelength are swept and normalized by the HCM period. Only the duty cycle is fixed at 0.61. The white stripes in Fig. 2(a) indicate mode resonance; the curved sharp color change patterns indicate mode resonance. For oblique-angle incidence, an odd mode resonance appears, as illustrated in Fig. 2(b). For both normal incidence and oblique angle incidence cases, the reflectivity contour plots show every clear cutoff behavior, as highlighted Fig. 2(a) and 2(b). In the deep subwavelength region, where is much larger than the averaged refractive index, only the fundamental mode is allowed. The diffraction under this region can be modeled by the average index method and the reflection is predicted by the thin film interference, as illustrated in the region to the right of the cutoff line in Fig. 2(a). When is smaller than the cutoff limit, the higher order modes are allowed, creating the chessboard pattern in the vs contour plot.
When a submicron waveguide is placed underneath the HCM structure, light coupling from the HCM to waveguide will occur when the aforementioned phase-matching condition is satisfied. For the surface normal incidence, the condition is . Under this condition, we observe an abrupt change in the plotted reflectivity spectrum due to the enhanced coupling. Because the phase matching is independent from the HCM thickness, the abrupt reflectivity change in the spectrum exists for all HCG thickness with the phase matching period, creating an additional vertical line in Fig. 2(c).
By tuning the HCM coupler thickness and duty cycle, the metastructure resonance and coupling to the waveguide can happen at the same wavelength. This condition is represented by the intersection of the vertical line and the resonance patterns in Fig. 2(c), and indicates that phase matching has occurred. We see that this vertical line intersects with the HCM resonance lines. At these intersection points, the curves repel one another, as shown in Fig. 3(a). This “anti-crossing” behavior creates a forbidden zone; the stronger the coupling, the wider the forbidden zone. Such anti-crossing effects are commonly observed in other physical systems, for example in coupled quantum-dot cavities  and photonic crystals , and signify strong coupling between different modes. At the center of the forbidden zone the real value for kz is no longer allowed, indicating that vertical propagation of light is forbidden and all incoming light must be transferred to the waveguide. The field profile at the center of anti-crossing is plotted in Fig. 3(b).
3. HCM vertical optical coupler
In order to verify the light coupling mechanism and derive coupling efficiencies, finite element time domain (FDTD) simulations  were performed. In these simulations, the HCM-based structure is made from silicon and the waveguide is made from silicon-on-insulator. The coupler is designed to couple incoming light of wavelength 1.55 μm. We use TE-mode light for the purposes of illustration, where the electrical field is along the y-direction. For light coupling from surface normal to in-plane, and a waveguide thickness of 100 nm, the HCM period is 720 nm and duty cycle is 0.61. The 100nm thickness is selected by the consideration of our fabrication process readiness. Nowadays, the silicon photonics foundries use SOI thickness ranging from 50nm to 450nm. Our design method is applicable to all thickness with the different optimization on coupler dimension and low index gap thickness, to make the phase matching coincide with the HCM resonance.
First, we simulate the coupling for a wide waveguide (of width 15 μm) composed of straight semiconductor bars. The gap between the HCM structure and waveguide is set to 265 nm. Using three-dimensional FDTD simulations, we can derive coupling efficiency as a function of the wavelength of the incident light and the thickness of the HCM coupler. By combining this FDTD simulation output with the anti-crossing curves calculated using rigorous coupled wave analysis (see  for more details), we confirm that the light coupling efficiency is strongly enhanced at the anti-crossing gap, as shown in Fig. 3(c). At an optimized thickness of 963 nm, the maximal light coupling efficiency is 93%, with a bandwidth of 3dB (48 nm). The field profile and coupling efficiency spectrum are shown in Fig. 4(a). For surface-normal incident light coupled into the waveguide, a small fraction of light in the waveguide is seen to propagate out of the coupling region outside of the coupler. The actual light coupling efficiency between the HCM and waveguide is therefore slightly larger than the figure of 93% measured. To uncover this “true” efficiency value, two identical mode-matched light sources are used into the waveguide symmetrically and the light output in the vertical direction is measured. In this configuration, the peak efficiency is measured to be 98% with a 3-dB (70-nm) bandwidth, as shown in Fig. 4(b). The waveguide incidence configuration shows large bandwidth comparing with vertical incidence due to the different scattering condition at the edge of the coupler.
For asymmetrical incidence, unlike the configuration shown in Fig. 4(b) with two identical light source inputs, we configure the incidence light from one of the waveguide ports. In this case, the asymmetric resonant mode will be involved in the coupling mechanism. With this set-up, we can choose to couple the light in two ways: into out-of-plane space or back to the waveguide. For light coupled into out-of-plane space, the HCM is designed with , and . The values are selected by searching for the anti-crossing region based on the same method for the symmetric coupler. The simulated data are shown in Fig. 5(a). In this case of asymmetrical incident light, the largest coupling efficiency that can be achieved is 96%, with an ultra-large 1dB bandwidth of 170 nm. Note the output light amplitude decays along the x-direction in this structure. For the purposes of coupling to other optical components such as optical fibers, the HCM structure can be chirped to provide better mode matching . For light coupled back to the waveguide, the HCM can serve as a reflector for light within the waveguide. For a HCM with , and , incident light is reflected back (with the identical transverse mode) with 98% reflectivity and a 1 dB bandwidth of 37 nm. The reflectivity shows similar flat band shape as Bragg reflector , because the HCM structure is essentially coupling the light into its asymmetric mode and creating the reflection by its in-plane periodicity.
The results shown in Fig. 4 and Fig. 5 demonstrate the basic functionality of our light coupling approach – efficient on-chip light coupling and reflection. These functionalities can be combined in interesting and practically useful ways.
One such example is the combination of a coupler with a waveguide reflector, which enables incoming light to be coupled into a preferred direction. The schematic of such a set-up is shown in Fig. 1(a). A waveguide reflector, which is designed to have the same thickness as the vertical coupler, is placed at the forbidden output for one waveguide direction. By optimizing the distance between the reflector and coupler, our FDTD simulations show that incoming light can be directed (coupled) from the surface-normal to a specific in-plane output direction with an efficiency of 88%. A natural application of this set-up is to integrate a multi-wavelength vertical-cavity-surface-emitting-laser (VCSEL) array onto a PIC for the purposes of on-chip wavelength-division multiplexing.
Another example involves using a circular outline coupler to fit the mode profile of a curved optical fiber as a way of minimizing waveguide taper length from the narrow waveguide to the light-coupling region. Due to the compactness of PICs, single-mode silicon photonic wires are usually very narrow (500 nm in diameter). However, because the input light aperture is much larger (for the purposes of reducing light losses) – typically around 10 μm for optical fiber, for example – the adiabatic transition taper angle is very small (approximately 1°). This means that the tapered waveguide has to be hundreds of microns in length, which is impractical for use in PICs. Adopting a focusing coupler configuration , in which the coupler is curved to focus the wave-front inside the taper region, enables a larger taper angle to be used, which translates to low loss. By choosing the HCM coupler to have a circular profile, the coupler can be made to match the optical fiber. With such a design, an 89% coupling efficiency is achieved with a 26° taper angle. The near-field output profile of the coupler is shown in Fig. 6(b) (blue curve). This configuration enables the use of a tapered waveguide that is ten times shorter.
4. HCM WDM multiplexer
The input-output (IO) bandwidth of the network system for the high performance computers and data centers is stimulating the development of the optical interconnections. From the first optical interconnection implemented in the super computer in 2005, the number of optical links in a high performance computing system has grown from thousands to millions . As of such dramatically fast growth trend, reducing the physical volume of the data links and the cost on fibers are important considerations for the future network systems. The wavelength division multiplexing (WDM) technology enables multiple channel data transmission in a single fiber-optic link and can dramatically increase the aggregate data rate . On the other hand, the tunable VCSEL array  provides the possibility to do chip level integration between active multi-wavelength laser source and photonic integrated circuits and reduce the cost of the WDM optical links. The conventional multiplexer (MUX), such as array waveguide grating multiplexer (AWG MUX) , has a fixed discrete wavelength grid. The wavelength of each channel is critically restricted. It diminishes the advantage of the tunable laser source, which desires the continuous wavelength multiplexing. The routing on the photonic chip is limited under this configuration, especially when the photonic circuit has high complexity.
As demonstrated in the previous section, the HCM vertical coupler can achieve ultra-high efficiency. Here, we add the periodicity in the additional dimension to the HCM to couple the light signal from the different channels with different wavelength into a single optical fiber. Figure 7(a) illustrates the schematic of the HCM MUX. Similar to the HCM vertical coupler configuration, the HCM is sitting on the waveguide with a low refractive index gap. However, the HCM in this case is periodic in two orthogonal in-plane directions to enable the vertical light coupling from four waveguide inputs. Any wavelength within the vertical coupling bandwidth is efficiently coupled into the optical fiber in the normal direction. Figure 7(b) shows the integration scheme between the tunable VCSEL arrays with the PIC through the proposed HCM MUX. The tunable VCSEL array bonds onto a set of the HCM vertical couplers to couple the light into the PIC. The light signal in each waveguide channel can go through the optical signal processing components, such as modulators. The signal process is not illustrated in the schematic. The proposed HCM MUX, simultaneously achieving wavelength multiplexing and efficient light coupling, enables the output coupling to the optical fiber.
The HCM MUX design follows the same method as the HCM vertical coupler, with the superposition of the periodicity in the orthogonal in-plane dimensions. The device can be analyzed as a 6-port device, with four in-plane waveguide ports (noted as C1 to C4), one port for fiber input/output (noted as T) and one port for back scattering (noted as B). Figure 8 illustrates the port configurations. When the waveguides have the same geometries, the scattering coefficients have rotational symmetry for to waveguide ports.
For the silicon waveguide with 100 nm thickness, the design for HCM MUX is , and . The low index gap is 220 nm. The coupling coefficients are simulated with FDTD method, with the configuration illustrated in Fig. 9(a). The incidence light source is placed in waveguide channel 1. The coupling coefficients, including for vertical coupling, , and for cross channel coupling and for back reflection, are shown in Fig. 9(b). Due to the rotational symmetry, the simulation result reveals all of the scattering matrix elements relevant to four waveguides. The vertical coupling efficiency has maximum value of 90% and 35 nm 1dB bandwidth, which is sufficient to cover the entire C-band for WDM applications. The output light can be slanted from the surface normal direction with single side incidence, as shown in Fig. 5(a). To ensure the fiber is able to collect the output light from all waveguide incidence, we recommend implementing the lens fiber for its large NA and the ability to couple light from a larger range of solid angle. In the meanwhile, the isolation to other ports are suppressed below −10dB for opposite port and below −25dB for perpendicular ports.
To illustrate the device working as a multiplexer, four narrow band light sources with peak power normalized to 0 dB, are placed at four waveguide channels. Figure 10(a) shows the spectrum of the fiber output, where all wavelengths are coupled to the fiber with ultra-high efficiency. The spectrum of the scattered light in channel 1 is shown in Fig. 10(b). It shows the reflection () and transmission from opposite channel (C3, ) are below −10dB and the scatter from the perpendicular channels are below −30dB.
Such structure reduces the MUX size to 10 micro meter scale and keeps the high coupling efficiency between on-chip waveguides and fibers and high isolation between different channels. Because the light coupling between one specific channel and the surface normal direction has no dependence on the optical structures of other channels, the proposed MUX can work at any wavelength within the high-coupling-efficiency bandwidth. Because there is no wavelength sequence and port location requirement for the input channels, this MUX is uniquely well suited for combining a tunable laser array. This function is being sought-after but has not be achieved with traditional grating-based WDM MUX.
5. Discussion and conclusion
In summary, we have demonstrated that it is possible to couple light very strongly from a high-refractive-index-contrast subwavelength metastructure to a submicron waveguide, as is typically used in an optical integrated circuit set-up. Coupling efficiencies of 93% are attainable. This represents an improvement in coupling efficiency beyond 20% relative to existing approaches, and offers a simpler design that lends itself to integration with PICs. The enhanced light coupling arises as a result of the optical resonance inside the cavity provided by the HCM. The HCM can be designed to act as a coupler between on-chip light and off-chip light or as a reflector for light within a waveguide. By combining such two functionalities, more advanced optical devices can be conceived. For instance, we can implement a single-layer HCM structure in an on-chip, in-plane cavity surface emitting laser, where the reflection mirrors and the output coupler all realized by the HCM. The device eliminates the need for any etching on the active material. This approach could lead to advanced photonic integrated circuits where light coupling is no longer an issue. The two-dimensional periodic HCM can simultaneously enable high efficiency vertical coupling for light propagating in the orthogonal directions in the PIC. Based on this unique feature, we demonstrate a high efficiency, ultra-compact WDM MUX with continuous wavelength response, exceeding the limits on the wavelength grid and sequence for the conventional AWG MUX, making it uniquely well suited for tunable laser and PIC integrated WDM applications.
NSF Award 0939514; Tsinghua-Berkeley Shenzhen Institute; SinBeRISE program NRF-CRP14-2014-03.
We thank Vadim Karagodsky for the helpful discussion to start this project.
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